Why yes, yes I have got a bit of a tan, thank you for noticing. The lady wife and I have just returned from a week-long honeymoon in New York. Yes, it was lovely. No, we didn't get you anything. We were far too busy trying to cope with navigating the real world.

As with any jaunt that takes us out of the apartment for more than a few hours, this adventure began with tightly-regimented blind panic. Lists were scrutinised, clothes were Tetris-ed into luggage, passports and dollars assigned to specific pockets and pouches. And most importantly of all, one little thing was checked and double checked: that data-roaming was turned off on both our iPhones.

In theory, Apple's shiny pocket butler (yes, that's correct) is the ultimate travelling companion, equipped with all manner of adventurer's tools and guides. However, network providers see things differently. Using your iPhone as an iPhone anywhere but your home country is an extortionate, baffling ordeal. You can either pay £OUCH per MB of data used, or get a "data bolt-on" for £ITBURNSITBURNS. And all this assumes you have the foggiest idea how much data every single app, website and email you dare to look at uses.

Rather than taint our trip by having to always contemplate such data-accountancy, we bravely chose to turn data-roaming off. What impact could this possibly have? We'll be in New York for crying out loud, we might as well leave our iPhones at home! Freedom! Let's live for a week without being shackled to our … no. No that's too much. Let's not be rash. Best to take them. Just in case. Let's just make sure data-roaming is turned off.

The trip began with a baptism of fire: never mind data-roaming, on the flight over we had to enter the fabled Airplane Mode. An announcement vaguely instructed us that some models of phone would have to be switched off altogether. How off do they want my phone to be? Could I still listen to music? Would spelling dirty words in Spelltower – a noble pursuit – somehow interfere with the navigation system? Best to be safe, I thought: turn phone off, put it away, don't do anything that might result in you having to eat the frozen remains of your fellow passengers. So, no iPhone. For several hours. It didn't feel right.

After a long and restless flight spent worrying that my inactivity on Twitter might have led to my account being suspended, we reached JFK. And now we had to get from JFK to the hotel. No worries, I'll just Goog— ah crap. There was no avoiding it: I'd have to ask a human being how to get somewhere. Englishman abroad Hugh-Grantisms: activated.

Eventually, after much bumbling and hair-flopping, we reached the hotel (The Library, a smashing place chosen primarily because it's near where they shot Ghostbusters and The Avengers. Who says romance is dead?) and decided to explore our surroundings, have a bit of a wander. With a map. A map made of paper.

Yes, there are many city guide apps that work offline, but we decided to embrace the old-fashioned tourism technique of using printed maps and getting a bit lost. We weren't completely offline: fortunately the hotel had wifi, so before stepping outside we did a bit of preliminary research and jotted down various addresses and subway stations on the back of my hand. Skin inked, outside we went.

And … it was great, liberating. Here we were, hands-free, looking at this incredible city in the best way possible. We were discovering things for ourselves, not checking emails or anything. We even managed to eat something without posting a picture of it to Instagram. Every now and then we'd refer to our trusty Wallpaper guide or to one of the various Herb Lester maps I had about my person, but it actually felt like we were exploring rather than being guided.

Throughout the week, we adjusted to this new eyes-open, apps-closed way of life. Back at the hotel, we'd give various social networks a quick glance (no need to go completely cold turkey – we're not savages), but outside, the iPhones mostly stayed holstered. Mostly.

One app that proved invaluable was New York City Compass (basically a skin for the iPhone's built-in, non-networked compass), which very simply tells you if you're facing Uptown or Downtown, East Side or West Side. In the big grid of Manahattan, this is invaluable, as it's a bit too easy to get completely disorientated when you step out of a subway. I don't mind getting a bit lost, but sometimes its nice to know if you're facing the right way (henceforth, this shall be the Benneworth-Gray family motto).

Every now and then something simply needed to be Googled – usually a bus stop or a film time – so we got into the habit of diving into a Prolific Hideously Syrupy Coffee Co. and piggybacking on their wifi for a couple of minutes while subjecting ourselves to their brown goop and trying to fathom the tipping protocol.

By the end of the week, we were almost accustomed to this way of life, but end-of-holiday-homesickness was kicking in (I started getting angry that nowhere sold Tunnock's Caramel bars), and the security blanket of our UK network was beckoning. Stepping off the plane at Gatwick, it was oddly reassuring to see the "3G" appear in the corner of my screen, but my time offline had been something of a revelation.

Abroad or not, sending your phone on an Airplane Mode holiday every now and then is good for you. Stop being connected, look up and get lost. Ooh, that's quite good … I have to tweet that … now where's my phone?